Sylvia Byrd

2022-07-02

How can the energy of a magnetic field spread at speed of light?

I would like to solve one question. Suppose that we have a point charge. Then we apply a force on it, and as it accelerates, it emits electromagnetic waves and is pushed back due to Abraham-Lorentz force. But then, when we drop it and it moves at constant speed, it starts to create a magnetic field that spreads at speed of light. So as the field occupies more volume, it increases its energy but we are not giving any energy as we have dropped it. So, where does this energy come from?

I would like to solve one question. Suppose that we have a point charge. Then we apply a force on it, and as it accelerates, it emits electromagnetic waves and is pushed back due to Abraham-Lorentz force. But then, when we drop it and it moves at constant speed, it starts to create a magnetic field that spreads at speed of light. So as the field occupies more volume, it increases its energy but we are not giving any energy as we have dropped it. So, where does this energy come from?

Nicolas Calhoun

Beginner2022-07-03Added 15 answers

As you've probably noticed, the formula

$Energy\sim \int {c}^{2}|\overrightarrow{B}{|}^{2}+|\overrightarrow{E}{|}^{2}dV$

appears to change with time.

But it's a bit more complicated than that. The electric field of a moving particle is different from that of a stationary particle (going as ${\overrightarrow{E}}_{\perp}^{\prime}=\mathrm{cosh}\varphi \cdot {\overrightarrow{E}}_{\perp}$ after lorentz transform). So while the magnetic field is getting "refreshed" and increasing, the electric field is getting refreshed and overall decreasing in such a way that the total energy remains constant.

That doesn't mean, however, that the total energy stored in the fields remains the same, ${E}^{2}-{c}^{2}{B}^{2}$ is the only lorentz invariant quality that will be the same for a stationary vs. moving point charge.

$Energy\sim \int {c}^{2}|\overrightarrow{B}{|}^{2}+|\overrightarrow{E}{|}^{2}dV$

appears to change with time.

But it's a bit more complicated than that. The electric field of a moving particle is different from that of a stationary particle (going as ${\overrightarrow{E}}_{\perp}^{\prime}=\mathrm{cosh}\varphi \cdot {\overrightarrow{E}}_{\perp}$ after lorentz transform). So while the magnetic field is getting "refreshed" and increasing, the electric field is getting refreshed and overall decreasing in such a way that the total energy remains constant.

That doesn't mean, however, that the total energy stored in the fields remains the same, ${E}^{2}-{c}^{2}{B}^{2}$ is the only lorentz invariant quality that will be the same for a stationary vs. moving point charge.

The product of the ages, in years, of three (3) teenagers os 4590. None of the have the sane age. What are the ages of the teenagers???

Use the row of numbers shown below to generate 12 random numbers between 01 and 99

78038 18022 84755 23146 12720 70910 49732 79606

Starting at the beginning of the row, what are the first 12 numbers between 01 and 99 in the sample?How many different 10 letter words (real or imaginary) can be formed from the following letters

H,T,G,B,X,X,T,L,N,J.Is every straight line the graph of a function?

For the 1s orbital of the Hydrogen atom, the radial wave function is given as: $R(r)=\frac{1}{\sqrt{\pi}}(\frac{1}{{a}_{O}}{)}^{\frac{3}{2}}{e}^{\frac{-r}{{a}_{O}}}$ (Where ${a}_{O}=0.529$ ∘A)

The ratio of radial probability density of finding an electron at $r={a}_{O}$ to the radial probability density of finding an electron at the nucleus is given as ($x.{e}^{-y}$). Calculate the value of (x+y).Find the sets $A$ and $B$ if $\frac{A}{B}=\left(1,5,7,8\right),\frac{B}{A}=\left(2,10\right)$ and $A\cap B=\left(3,6,9\right)$. Are they unique?

What are the characteristics of a good hypothesis?

If x is 60% of y, find $\frac{x}{y-x}$.

A)$\frac{1}{2}$

B)$\frac{3}{2}$

C)$\frac{7}{2}$

D)$\frac{5}{2}$The numbers of significant figures in $9.1\times {10}^{-31}kg$ are:

A)Two

B)Three

C)Ten

D)Thirty oneWhat is positive acceleration?

Is power scalar or vector?

What is the five-step process for hypothesis testing?

How to calculate Type 1 error and Type 2 error probabilities?

How long will it take to drive 450 km if you are driving at a speed of 50 km per hour?

1) 9 Hours

2) 3.5 Hours

3) 6 Hours

4) 12.5 HoursWhat is the square root of 106?